Successful integration of CFD and experiments in fluid dynamics: the computational investigator point of view

Transcription

1 Successful integration of CFD and experiments in fluid dynamics: the computational investigator point of view G. Degrez, W. Dieudonné, T. Magin for Fluid Dynamics Page 1 of 41 Service de Mécanique des fluides, Université Libre de Bruxelles Integrating CFD and Experiments in Aerodynamics Symposium University of Glasgow, Sep. 8th 9th, 2003

2 1 Introduction 4 2 Hypersonic flow over a blunted cone-flare Wind tunnel, model & experimental techniques Checking flow axisymmetry & repeatability Numerical method Computational results Effect of freestream non-uniformities Flows in ICP facilities Determination of wall catalytic efficiency by combined experiments and computations Numerical study of the flow around a cooled pitot probe Page 2 of 41

3 4 Conclusions 40 Page 3 of 41

4 1 Introduction Over the past 30 to 40 years, revolution in scientific and engineering practise brought by the tremendous development of numerical simulation. In aerodynamics, CFD is now ubiquitous in research and design. But development of CFD so fast that standards of good use have not emerged yet, or at least are not widespread. A fundamental question: reliability of numerical simulations important development of verification and validation (V & V) activities, elaboration of V & V standards. Page 4 of 41

5 A trend in CFD simulations: increasingly complex physical problems: 2-phase flows, reacting flows, high temperature flows, complex turbulent flows, which require increasingly complex physical models. Integrated computational and experimental studies very useful to calibrate physical models, for parameter identification problems. of the talk ˆ Validation study: hypersonic flow over a blunted cone/flare, ˆ Flows in inductively coupled plasma (ICP) facilities for thermal protection material (TPM) testing: determination of a TPM sample catalytic activity, analysis of pitot pressure measurements with a cooled pitot probe. Page 5 of 41

6 2 Hypersonic flow over a blunted cone-flare Rationale: ˆ flow problem exhibiting several features of flows over reentry vehicles, bow shock wave & associated entropy layer, shock induced separation. ˆ axisymmetric flow problem, to allow thorough grid refinement study Page 6 of 41

7 2.1 Wind tunnel, model & experimental techniques Figure 1: VKI H3 hypersonic wind tunnel Page 7 of 41 P 0 T 0 M MPa 550 K 6 Table 1: Operating conditions

8 R=3.5 Ø10.53 Ø6 h6 Ø10.53 M ± M50 x Ø6 H7 M Pressure taps at 90, 80, 270º 17.5º 15 ±Ø59 Ø Figure 2: Blunt cone-flare model with pressure taps location Experimental techniques Pressure Electronic pressure scanner δp = 7.3% Heat fluxes IR thermography δs t = 11.5% Page 8 of 41

9 2.2 Checking flow axisymmetry & repeatability 4.0 yaw=+0.10 o, R=0 o yaw=+0.10 o, R=180 o yaw=+0.10 o, R=90 o yaw=+0.10 o, R=270 o 3.0 P wall /P first tap Page 9 of Distance from the nose [mm] Figure 3: Pressure distributions for 4 azimuthal positions

10 Sensitivity to pitch/yaw Figure 4: Effect of yaw (0.25 ) on IR thermogram Page 10 of 41

11 Repeatability bars run 1 10 bars run Pressure [mm H 2 O] Page 11 of X location [mm] Figure 5: Repeatability of consecutive runs

12 2.3 Numerical method ˆ Multiblock structured cell-centered 2D/axisymmetric finite volume solver Grids ˆ Inviscid fluxes discretized using upwind Riemann solvers. Hybrid upwind splitting scheme used in present study ˆ algebraic, one-equation and two-equation turbulence models implemented. Spalart-Allmaras turbulence model used for the wind tunnel nozzle flow computations. Page 12 of 41 Grid level coarse medium fine Size

13 2.4 Computational results Linear Contour Plot. Mach number lines Step = y x Page 13 of 41 Figure 6: Computed Mach number contours on fine grid

14 0.25 Coarse 101x21 Medium 201x41 Fine 401x e 03 Coarse 101x21 Medium 201x41 Fine 401x e 03 Cp 0.15 St 1.00e e distance from the nose [m] (a) pressure coefficient distribution 0.00e Distance from the nose [m] (b) Stanton number distribution Figure 7: Computed pressure and heat flux distributions Page 14 of 41

15 Grid coarse medium fine x sep /x hinge x reat /x hinge Table 2: Separation and reattachment point locations Conclusion: solution not grid-converged in recirculation bubble/ downstream of reattachment. Page 15 of 41

16 Experiment Fine grid (401x81) Experiment Fine grid (401x81) Cp St Distance from the nose [m] (a) pressure coefficient distribution Distance from the nose [m] (b) Stanton number distribution Figure 8: Comparison with experiments Page 16 of 41 Conclusion: disagreement not only in recirculation region, but also on cone surface (heat flux)

17 2.5 Effect of freestream non-uniformities Problem geometry Figure 9: H3 nozzle geometry laminar computations turbulent computations Grid level Medium Fine Medium Fine nozzle & test section tunnel chamber Table 3: Nozzle grids Page 17 of 41

18 6.4 H3 - Laminar - Coarse (231x65) H3 - Laminar - Medium (461x129) H3 - Laminar - Fine (921x129) Experiment H3 Turbulent xt=0.04m Experiment Mach Mach number X [m] distance from throat X [m] distance from the throat (a) laminar computation (b) turbulent computation Figure 10: Centerline Mach number distributions Page 18 of 41 Conclusion: turbulent computation with x t = 0.04 m in agreement with experiments

19 Confirmation Pt2/P exp x=0.768m exp x=0.813m exp x=0.858m exp x=0.898m num x=0.768m num x=0.813m num x=0.858m num x=0.898m Page 19 of Y [m] distance from the center line Figure 11: Pitot pressure profiles across jet (x t = 0.04m)

20 Mach Number Line Contours Fmin Fst Finc Fmax Figure 12: Mach number contours near nozzle throat Figure 13: Mach number contours in nozzle Page 20 of Figure 14: Mach number contours in jet flow

21 Mach number Mach Number Line Contours X [m] distance from the throat Fmin Fst Finc Fmax Figure 15: Mach number distribution on cone-flare inflow boundary y Page 21 of x Figure 16: Mach number contours for model in wind tunnel

22 e+04 Experiment Experiment Computation: uniform flow Computation: uniform flow Computation: varying flow Computation: variable flow e+04 Pressure [Pa] 3000 Qw [W/m2] 1.0e e X [m] distance from the nose 0.0e X [m] distance from the nose (a) pressure coefficient distribution (b) Stanton number distribution Figure 17: Comparison with experiments Page 22 of 41 Observation: computed heat flux on cone in agreement with experiments

23 Uniform Mach 5.9 inflow conputation Experiment 1.5e-03 Num. Mach=5.9 Num. Mach=6.0 St 1.0e e e Distance from the nose [m] Page 23 of 41 Figure 18: Stanton number distributions, uniform M = 5.90 inflow

24 3 Flows in ICP facilities 3.1 Determination of wall catalytic efficiency by combined experiments and computations Motivation ˆ Re-entry vehicles must be protected by heat shields made of Thermal Protection Materials (TPM); ˆ Heat shield size controlled by wall heat flux, which strongly depends on the heat shield surface catalytic efficiency. Need to know the catalytic efficiency of TPS materials Page 24 of 41

25 BUT ˆ TPS materials catalytic efficiency in flight conditions cannot be reliably calculated a priori using some physico-chemical theory or computational model, or measured directly. it has to be determined indirectly through its effect on wall heat flux by experimental testing on TPS samples in high enthalpy facilities producing flow conditions close to flight conditions. ˆ ICP facilities particularly well suited for such testing because of very high chemical purity of the plasmas (absence of metallic impurities due to electrode erosion). Motivation for the construction of VKI s large (1.2MW/ 160mm diameter) ICP facility. Page 25 of 41

26 3.1.2 The IPM methodology JJ II J I Page 26 of 41 Figure 19: Heat flux probe in VKI Plasmatron (air, p = 75 kpa, P = 250 kw, qm = 8 gs 1, no swirl)

27 Assuming the flow to be in LTE outside the thermal/chemical boundary layer around the TPS sample, the stagnation point heat flux can be written as q w = f (p e, h e, ( v r ) e, δ, u e x ( v r ) e, T w, γ w ) (1) outer thermodynamic state radial velocity gradient boundary layer thickness axial acceleration wall properties If all other quantities are know, and a model is available to compute the stagnation point heat flux, the catalytic activity γ w can be determined ˆ p e, q w, T w measured experimentally, ˆ other quantities obtained from a LTE flow computation? Page 27 of 41

28 ICP facility JJ II J I Page 28 of 41 mass flow, Operational parameters pressure, power injected in plasma.

29 LTE flow computational model ˆ Multiblock coupled hydrodynamic/em cell-centered finite volume solver, ˆ 2D (axisymmetric) EM field model (important for low aspect ratio torches) ˆ 2nd order pressure-stabilized collocated formulation. ˆ thermodynamic properties computed on-the-fly using statistical thermodynamics; transport properties computed from Chapman-Enskog perturbative theory. Page 29 of 41

30 Illustrative result Figure 20: Temperature field in VKI pilot ICP facility (air, p = kpa, P = 4 kw, q m = 0.55 gs 1, no swirl) Observation: flow pattern depends (almost) exclusively on mass flow Π 1 δ R, Π 2 u e x ( v r ) e/( v r )2 e, independent of pressure/power combinations. Page 30 of 41

31 Reconstruction of boundary layer edge properties Stagnation point heat flux (Eqn 1) can be re-expressed as q w = f (p e, h e, ( v r ) e, Π 1, Π 2, γ w, T w ) (2) Performing an auxiliary heat flux measurement on a on a cold wall (T w 300 to 400 K) reference heat flux probe assumed to be fully catalytic (γ w = 1), and the non-dimensional parameters Π 1,2 obtained from an LTE flow simulation, this becomes an equation in 2 unknowns, i.e. h e and ( v r ) e. To close the problem, a second auxiliary measurement is performed, namely a pitot pressure measurement using a cooled pitot probe. In a cold high Reynolds number flow, Page 31 of 41 p = p pitot p = ρ eu 2 e 2

32 For a cooled pitot probe in a hot low Reynolds number plasma flow ρ e u 2 e p = K p (3) 2 where the impact parameter K p can a priori depend on flow Reynolds number and freestream/wall temperature combination. The relationship between K p and these parameters was the subject of a specific computational study (section 3.2). Eqn 3 can be rewritten as 2 2 p u e ( ρ e R( v r ) ) 2 = K p R( v e r ) (4) e where there appears an additional non-dimensional parameter Page 32 of 41 Π 4 = R( v/ r) e u e (5)

33 which is also obtained from the LTE flow simulation in the ICP facility. The boundary layer edge enthalpy h e and velocity gradient ( v r ) e can then be reconstructed by solving the system q w,aux = f (( v r ) e, h e, p e, Π 1, Π 2, T w,aux, γ w = 1) (6) p = K ( p 2Π ρ 2 e(p e, h e ) R( v ) 2 4 r ) e (7) LTE flow simulation output experimental measurements unknowns where the stagnation point heat flux function f is obtained by running a chemical non-equilibrium one-dimensional solver for the self-similar axisymmetric stagnation line flow (4th order compact Hermitian finite difference solver). Page 33 of 41

34 Calculation of heat flux abacus (optional) Run stagnation line flow solver for various T w, γ w combinations using the reconstructed boundary layer edge properties q w = f (p e, h e, ( v r ) e, Π 1, Π 2, γ w, T w ) produce a heat flux abacus. Determination of TPS material catalytic activity From experimental measurement of a TPS sample wall temperature and stagnation point heat flux (T w, q w ) deduce γ w by solving q w = f (( v r ) e, h e, p e, Π 1, Π 2, T w, γ w ) (8) or graphically from heat flux abacus. Page 34 of 41

35 3.1.3 Summary & illustrative application CATALYTIC ACTIVITY DETERMINATION METHODOLOGY LTE VISCOUS FLOW SIMULATION High enthalpy flow simulation around model 3 dimensionless hydrodynamic parameters ( Πi) Calculation of the wall heat flux for various catalytic efficiency ( γ w ) /wall temperature combinations using non equilibrium BL solver qw RECONSTRUCTION OF THE PLASMA JET CHARACTERISTICS (he, dv/dr) Non equilibrium BL computation qw (he,dv/dr, Π 1, Π γ 2, w,tw) = BL Hydrodynamics Π ρ 3 e (he, p) (R dv/dr) = Pexp. 2 γ w = 1 qw) exp. EXPERIMENTS Heat flux (qw) and Pitot presure ( P) measurements on a fully catalytic ( γw) cold wall model Test measurements on a TPS material sample Page 35 of 41 γ w = 0 Tw catalytic efficiency identification

36 LTE computation Input parameters: axial injection, p = 10 kpa, P = 75 kw, q m = 8 gs 1. Π 1 = Π 2 = Π 4 = Heat flux and pitot pressure measurements using a cooled copper probe Operating conditions: q m = 8 gs 1, p = 2.5 kpa, P el = 100 kw. p pitot p ref = 25 Pa, q w = kw m 2 Reconstruction of boundary layer edge properties Using K p = 1.1 and Gupta s chemical reaction model, we find h e = 13.85MJ kg 1 and ( v/ r) e = 3710 s 1 Page 36 of 41

37 Construction of heat flux abacus γ w =1 q w (MW/m2) γ w =0 γ w =0.1 γ w = γ w =0.001 frozen flow and γ w = T w (K) Page 37 of 41 Heat flux abacus for VKI Plasmatron with air, q m = 8 gs 1, p = 2.5 kpa, P el = 100 kw

38 TPS testing and determination of catalytic activity Measurement of heat flux and wall temperature of a quartz sample: q w = kw m 2, T w = K (see heat flux abacus). Iterating with boundary layer solver, we get γ w = Numerical study of the flow around a cooled pitot probe The value of the impact parameter K p in Eqn. 3 was determined from LTE flow computations. They showed that ˆ p t p ρu 2 /2 Page 38 of 41 p pitot p p t p 2 p ρ e u 2 s = K p

39 ˆ K p increases very slightly with decreasing wall temperature, ˆ K p increases with decreasing probe dimensions (low-reynolds number effect), ˆ K p in good agreement with cold flow correlation by Homann. CAVEAT In practise, one doesn t measure p = p pitot p but rather the difference between p pitot and some reference pressure (e.g. test chamber pressure). Computational results show that ˆ for axial injection, p ref p, ˆ for swirling injection, there can be differences up to 45% between p pitot p and p pitot p ref. Page 39 of 41 Correlations for K p inapplicable for swirling flows

40 4 Conclusions Examples of combined CFD and experimental studies carried out in the Aerospace department at the over the past few years have been presented. The main lessons learned from these studies are the following. hypersonic flow over a blunted cone/flare validation study ˆ careful model alignment to ensure flow axisymmetry extremely important; ˆ accurate knowledge of boundary conditions needed: discrepancies in computed and measured surface heat fluxes shown to be due to freestream non-uniformities. Page 40 of 41

41 Flows in ICP facilities ˆ synergetic use of two CFD models (LTE coupled hydrodynamic/em solver and 1D chemical non-equilibrium stagnation line solver) and experiments essential to determine TPMs catalytic activity; ˆ computational study of flow around a cooled pitot probe very useful for the data reduction of pitot pressure measurements Page 41 of 41